This paper presents a simple and easy way to obtain good estimates of the frequencies of spectral peaks in voiced sounds. The instantaneous frequency throughout the spectrum is calculated using an analytically derived window. Peaks are detected by examining the difference between the frequencies of spectral lines and their corresponding instantaneous frequencies. The instantaneous frequencies near peaks are used as estimates of their actual frequencies. The corresponding amplitude values are calculated from the Gabor transform at the estimated frequencies. The performance of the estimation of the frequencies using analytically derived windows has been verified using synthetic signals and musical sounds. This method gives a better estimate of the instantaneous frequency than commonly used methods and the resynthesis of sound from the additive parameters gives good results.